Arane $($D$)$ has roll, pitch and yaw angles respectively of $\frac{}{6},\frac{}{4},$ and $-\frac{}{6}.$ Its position in world

frame is $P_D^W=\left[\begin{array}{c}1\\ 1\\ 10\end{array}\right]$

a$)$ Write the homogeneous transformation matrix $A_D^W$ representing both the position and

orientation of the drone in world frame $W.$

b$)$ Write the homogeneous transformation matrix $A_W^D$ representing both the position and

orientation of the world frame $W$ in drone frame $D.$

A sensor mounted on the drone identifies an obstacle in $Q^D=\left[\begin{array}{c}2\\ 0\\ 0\end{array}\right].$

c$)$ Where is the obstacle in world frame $W?$

A map in $W$ indicates that the landing pad of the drone is in $G^W=\left[\begin{array}{c}10\\ 0\\ 0\end{array}\right].$

d$)$ where is the landing pad with respect to the drone $($i$.$e$.,G^D)?$